# A TV tower has a height of 100m.If the coverage range is to be made three times then by how much should the height of the tower be increased.

$\begin{array}{1 1}(a)\;500m\\(b)\; 600m\\(c)\;700m\\(d)\;800m\end{array}$

Covering range $R\propto \sqrt h$
(ie) $R^2\propto h$
If range is to be tripled
$R'=3R$
$\big(\large\frac{R}{3R}\big)^2=\frac{h}{h'}$
$\large\frac{1}{9}=\frac{h}{h'}$
$h'=9h$
Height of the tower initially $h=100m$
$h'=9\times 100$
$\;\;\;\;=900m$
$\therefore$ The height of the tower has to be increased by
$h'-h=900-100$
$\Rightarrow 800m$
Hence (d) is the correct answer.
answered Mar 17, 2014